Is it okay to use "babysit" verb in context of own kids?

The verb to babysit is now extending its original meaning ("to take  charge of a child while the parents are temporarily away") and is often used in the wide sense of 'to take care of anybody: any (including one's own) children, aged and disabled people, pets'.

The following sentence from Collin's Dictionary (https://www.dictionary.com/browse/babysit?s=t):

''Even more annoying, have you heard of a guy say he has to " babysit "  his children  when  his wife  has something to do?'' shows it's OK to say: 'I have to babysit my kids'.

According to Collin's Dictionary (https://www.dictionary.com/browse/babysit?s=t) the meaning of the verb 'to babysit' is very wide:

to take watchful responsibility for; tend

: It will be necessary  for someone to baby-sit the machine  until it is running  properly.

It depends on your role and attitude as a parent. If watching your kids isn't something you normally do, and/or you resent doing it, "babysit" would be appropriate. If it is something you do with some frequency, or even if it's not but you want to help her, then you would be "watching" your kids.